Question

The coefficient of (r – 1)^th, r^th, and (r + 1)^th terms in the expansion of (x + 1)ⁿ are in the ratio 1 : 3 : 5.

Answer 1

We know that co-effcients of (r – 1)^th, r^th and (r + 1)^th terms in the expansion of (x + 1)ⁿ are ⁿC_{r - 2} : ⁿC_{r - 1} and ⁿC_r respectively 

Now

⇒ 3n – 8r + 3 = 0 and n – 4r + 5 = 0 

Solving these for n, r we get, 

n = 7 and r = 3